Question: Express your answer as a mixed number simplified to lowest terms. $4\dfrac{1}{3}-2\dfrac{10}{17} = {?}$
Find a common denominator for the fractions: $= {4\dfrac{17}{51}}-{2\dfrac{30}{51}}$ Convert ${4\dfrac{17}{51}}$ to ${3 + \dfrac{51}{51} + \dfrac{17}{51}}$ So the problem becomes: ${3\dfrac{68}{51}}-{2\dfrac{30}{51}}$ Separate the whole numbers from the fractional parts: $= {3} + {\dfrac{68}{51}} - {2} - {\dfrac{30}{51}}$ Bring the whole numbers together and the fractions together: $= {3} - {2} + {\dfrac{68}{51}} - {\dfrac{30}{51}}$ Subtract the whole numbers: $=1 + {\dfrac{68}{51}} - {\dfrac{30}{51}}$ Subtract the fractions: $= 1+\dfrac{38}{51}$ Combine the whole and fractional parts into a mixed number: $= 1\dfrac{38}{51}$